What is the 20th term of the sequence that begins -2, 4, -8, 16...?

Question

campbell_st · Answer

well what is the common ratio r...?

texaschic101 · Answer

first you need to figure out if this is a geometric sequence or an arithmetic sequence. Can you do that ?

anonymous · Answer

No, I don't know how

anonymous · Answer

I don't know campbell_st

campbell_st · Answer

ok... try looking at the terms

-2 x ? = 4

4 x ? = -8

-8 x ? = 16

what do you think the value of ? is

anonymous · Answer

-2

texaschic101 · Answer

an arithmetic sequence....the numbers are determines by adding
a geometric sequence is determined by multiplying

what you have is a geometric sequence and you need to find the common ratio by dividing the second term by the first term.
4 / -2 = ?

correct...the ratio is -2 between each number

anonymous · Answer

Okay...

campbell_st · Answer

great, thats the common ratio r... 

the formula for a term in an geometric series is 

$$a_{n} = a \times r^{n - 1}$$

in your question n = 20 and a = -2 as well as r = -2

so you get

$$a_{20} = -2 \times (-2)^{20-1}$$

which simplifies to 

$$a_{20} = -2 \times (-2)^{19}$$

so put the right hand side of the equation into a calculator... as its written to find the 20th term

texaschic101 · Answer

now we will use the formula:
an = a1 * r^(n-1)
n = the term you want to find = 20
a1 = first term = -2
r = common ratio = -2

campbell_st.....you type fast...lol

anonymous · Answer

Wow thanks, that makes perfect sense Campbell_st! I got 1,048,576

anonymous · Answer

Thank you so much texaschic101!

texaschic101 · Answer

no problem...I didn't really do that much.. Read this...it will help http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm

anonymous · Answer

Oh you did :) Ok I will, thanks

texaschic101 · Answer

:)